Related Theory Research Of Fuzzy Clustering Based On Fuzzy Equivalent Matrix

The fuzzy clustering analysis technology based on Fuzzy Equivalent Matrix is widely used in real life, providing the basis of scientific decision for the production and life practice. In view of the three steps of fuzzy clustering, this paper made some related research work respectively.In the process of standardization of data, this paper proves that the original data matrix is translated by standard deviation and extreme deviation orderly, in fact, is equal to translated by extreme deviation only, and this paper gives applicable occasions of two kinds of transformation respectively.In the process of constructing fuzzy similar matrix, this paper puts forward the differential square inverse method; Considering phenomenon that difference of the influence degree of each attribute on the sample clustering will appear in practical problems, this paper introduces the weighted coefficient for 10 ways which determine the similarity coefficient respectively; For some construction method of fuzzy similar matrix which involved in the parameter, this paper proves that no matter how to choose value of the parameters in the formula, the final clustering results are the same; this paper gives the definition of Method’s equivalent and proves that the maximum minimum method is equal to the arithmetic average minimum method, the absolute value inverse method, the absolute value index method and the hamming distance method are equal and the differential square inverse method is equal to the Euclidean distance method.In a study of how to compute the transitive closure of fuzzy similar matrix, firstly, this paper puts forward a simple and direct algorithm, and describes the steps of the algorithm in detail; secondly, this paper describes the core principle of the algorithm in the form of theorem and gives theoretical proof; thirdly, this paper shows C++ program of the algorithm through three pseudo code segments and demonstrates that the time complexity of the algorithm for O(n2); finally, some complete comparison about applicable occasions and time complexity among the algorithm and other three methods is made respectively.Finally, a complete comparison among ten kinds of methods in the construction of the fuzzy similar matrix is made with three groups of data respectively, and then some better methods used in the construction of the fuzzy similar matrix are recommended through the summary and analysis of the result of the experiment; a comparative experiment among three methods in the computation of the transitive closure of fuzzy similar matrix is also made at the end of this paper, and the experimental results show that: the algorithm which is proposed by this paper has a better time efficiency.